OBIWAN PLACEBO VS. TREATMENT ANALYSIS REPORT

Setup

library(repro)
# load packages from yaml header
automate_load_packages()
# include external scripts
automate_load_scripts()

# load data
intern  <- automate_load_data(intern, read.csv, stringsAsFactors = T)
medic    <- automate_load_data(medic, read.csv, stringsAsFactors = T)
PAV      <- automate_load_data(PAV, read.csv, stringsAsFactors = T)
INST     <- automate_load_data(INST, read.csv, stringsAsFactors = T)
PIT      <- automate_load_data(PIT, read.csv, stringsAsFactors = T)
HED      <- automate_load_data(HED, read.csv, stringsAsFactors = T)
HED_fMRI <- automate_load_data(HED_fMRI, read.csv, stringsAsFactors = T)

x = session_info();  opts_chunk$set(echo = FALSE, warning = FALSE, message = FALSE) # set F for all


## we recommend running this is a fresh R session or restarting your current session
#install.packages("cmdstanr", repos = c("https://mc-stan.org/r-packages/", getOption("repos")))
#install_cmdstan()


# check_git(); check_make(); check_docker() #check if installed

sessio = session_info(); #opts_chunk$set(echo = F, message=F, warning=F) # set echo F for all

This file was automatically created via the Repro package (version 0.1.0) using R version 4.0.1 (2020-06-06)

Description

TODO blabla

Demographics

Summary statistics

	Placebo M (SD)/N (%)	Liraglutide M (SD)/N (%)	Test
BMI	35.08 (2.96)	35.74 (2.93)	t(df=47) = -0.78, p = .438, d = 0.22
AGE	40.27 (13.74)	38.61 (11.72)	t(df=47) = 0.45, p = .653, d = 0.13
GENDER			Chi-square = 0.35, df = 1, p = .556, Phi = 0.08
Men	10 (38.5)	7 (30.4)
Women	16 (61.5)	16 (69.6)

Biomedical data

Variable Selection

Box-plot of all biomedical predictors per intervention.

Recursive Feature Eliminations

## [1] "BMI_diff"    "BW_diff"     "reelin_diff" "GLP_diff"

Mediation analysis

Mediation Analysis: DV = Weight loss, IV = Intervention

		Estimates	95% CI	p
1	Indirect effect mediated through GLP_diff	0.017	(-0.280, 0.325)	0.919
2	Indirect effect mediated through reelin_diff	0.048	(-0.104, 0.249)	0.535
5	Direct effect	1.427***	(0.963, 1.909)	< 0.001
6	Total effect	1.492***	(1.021, 2.006)	< 0.001

Weight Loss

## [1] "Bayesian linear mixed model (estimated using MCMC sampling with  4  chains of 500  iterations and a warmup of 100 ) to predict weightLoss with intervention, gender, age, GLP_diff and reelin_diff (formula: weightLoss ~ intervention + gender + age + GLP_diff + reelin_diff). The model included id as random effect (formula: ~1 | id). Priors over parameters were set as normal (mean = 0.00, SD = 3.00), and student_t (location = 0.00, scale = 2.50) distributions"

## Summary of Posterior Distribution
## 
## Parameter    | Median |  MAD |        90% CI |     pd |  Rhat |     BF
## ----------------------------------------------------------------------
## intervention |   1.36 | 0.21 | [ 0.99, 1.75] |   100% | 1.010 | 407.30
## gender       |   0.16 | 0.20 | [-0.16, 0.48] | 78.25% | 1.000 |  0.092
## age          |  -0.27 | 0.20 | [-0.61, 0.01] | 92.69% | 1.004 |  0.193
## GLP_diff     |  -0.19 | 0.28 | [-0.68, 0.25] | 74.75% | 1.010 |  0.124
## reelin_diff  |  -0.02 | 0.31 | [-0.54, 0.48] | 52.50% | 1.014 |  0.108

## [1] "- b_intervention (Median = 1.36, 90% CI [0.99, 1.75]) has a 100.00% probability of being positive (> 0), 100.00% of being significant (> 0.09), and 99.94% of being large (> 0.54)"

## 
## ------------------------------------
##  ICC    N id   Observations    R2   
## ------ ------ -------------- -------
##  0.16    45         45        0.730 
## ------------------------------------

Plot Weight Loss

Weight Loss by intervention.

Pavlvovian Conditioning Task

Latency

Latency = time to detect the target (ms) & condition = CS+ or CS-

## [1] "Bayesian general linear mixed model (exgaussian family with a identity link) (estimated using MCMC sampling with  4 chains of 500 iterations and a warmup of 100 ) to predict Latency with condition, intervention, session, age, gender, BMI_V1, hungry, GLP_diff and reelin_diff (formula: RT ~ condition * intervention * session + age + gender + BMI_V1 + hungry + GLP_diff + reelin_diff). The model included condition, session, id and trialxcondition as random effects (formula: list(~condition * session | id, ~1 | trialxcondition)). Priors over parameters were set as normal (mean = 0.00, SD = 3.00), and student_t (location = 0.00, scale = 130.20) distributions"

## Summary of Posterior Distribution
## 
## Parameter                      | Median |  MAD |        90% CI |     pd |  Rhat |    BF
## ---------------------------------------------------------------------------------------
## condition                      |  -4.34 | 2.36 | [-8.22, 0.15] | 92.69% | 1.206 |  3.59
## intervention                   |   0.59 | 3.02 | [-4.49, 5.70] | 58.13% | 1.005 |  1.11
## session                        |   0.04 | 2.65 | [-4.47, 4.44] | 50.94% | 1.009 | 0.883
## age                            |   1.42 | 3.02 | [-3.57, 6.21] | 67.00% | 1.061 |  1.37
## gender                         |   0.36 | 2.91 | [-4.37, 5.22] | 55.38% | 1.015 | 0.977
## BMI_V1                         |   0.34 | 2.89 | [-4.85, 5.16] | 54.12% | 1.012 | 0.924
## hungry                         |  -1.76 | 2.82 | [-6.23, 3.08] | 73.12% | 1.046 |  1.26
## GLP_diff                       |  -0.55 | 2.85 | [-5.48, 3.95] | 57.56% | 1.029 | 0.924
## reelin_diff                    |  -0.22 | 3.00 | [-5.27, 4.80] | 52.94% | 1.005 |  1.07
## condition:intervention         |  -0.07 | 1.82 | [-3.40, 2.62] | 51.06% | 1.007 | 0.607
## condition:session              |  -1.65 | 1.90 | [-4.96, 1.44] | 78.44% | 1.076 |  1.05
## intervention:session           |  -1.71 | 2.52 | [-5.43, 2.81] | 74.81% | 1.029 | 0.953
## condition:intervention:session |   0.06 | 1.70 | [-2.50, 3.02] | 51.38% | 1.008 | 0.593

## [1] "- b_condition (Median = -4.34, 90% CI [-8.22, 0.15]) has a 92.69% probability of being negative (< 0), 92.50% of being significant (< -0.05), and 91.38% of being large (< -0.30)"                  
## [2] "- b_condition.intervention.session (Median = 0.06, 90% CI [-2.50, 3.02]) has a 51.38% probability of being positive (> 0), 50.38% of being significant (> 0.05), and 44.81% of being large (> 0.30)"

## 
## --------------------------------------------------------
##  ICC    N id   N trialxcondition   Observations    R2   
## ------ ------ ------------------- -------------- -------
##  1.00    50           20               3223       0.204 
## --------------------------------------------------------

Plot Latency

1. Posterior distribution by Pavlovian cue. B) Highest density interval (90% HDI) of the posterior distribution difference for the latency to respond between CS+ and CS-

Perceived liking (Pavlovian Cue)

Ratings = how pleasant is the clue (0-100, no repetitions) & condition = CS+ or CS-

## [1] "Bayesian linear mixed model (estimated using MCMC sampling with 4  chains of 500  iterations and a warmup of 100 )  to predict liking with condition, intervention, session, age, gender, BMI_V1, hungry, GLP_diff and reelin_diff (formula: liking ~ condition * intervention * session + age + gender + BMI_V1 + hungry + GLP_diff + reelin_diff). The model included condition, session and id as random effects (formula: ~condition * session | id). Priors over parameters were set as normal (mean = 0.00, SD = 3.00), and student_t (location = 0.00, scale = 15.10) distributions"

## Summary of Posterior Distribution
## 
## Parameter                      | Median |  MAD |         90% CI |     pd |  Rhat |     BF
## -----------------------------------------------------------------------------------------
## condition                      |   6.77 | 1.62 | [ 3.84,  9.34] |   100% | 1.008 | 298.81
## intervention                   |  -1.91 | 1.32 | [-4.01,  0.35] | 92.38% | 1.007 |   1.27
## session                        |  -1.94 | 1.02 | [-3.52, -0.13] | 96.56% | 0.998 |   2.22
## age                            |   1.58 | 1.16 | [-0.39,  3.54] | 89.31% | 1.004 |  0.867
## gender                         |   0.06 | 1.28 | [-2.00,  1.84] | 51.75% | 1.001 |  0.411
## BMI_V1                         |   0.34 | 1.24 | [-1.70,  2.35] | 61.44% | 1.002 |  0.435
## hungry                         |   4.63 | 1.14 | [ 2.77,  6.57] |   100% | 1.000 | 166.29
## GLP_diff                       |   0.47 | 1.55 | [-1.84,  3.00] | 62.19% | 1.000 |  0.579
## reelin_diff                    |  -0.46 | 1.55 | [-2.98,  2.20] | 61.06% | 1.005 |  0.560
## condition:intervention         |   0.45 | 1.55 | [-2.09,  3.18] | 61.62% | 1.007 |  0.548
## condition:session              |  -0.42 | 0.94 | [-1.96,  1.20] | 66.06% | 1.000 |  0.384
## intervention:session           |   0.31 | 0.96 | [-1.23,  1.89] | 62.62% | 0.999 |  0.351
## condition:intervention:session |   1.05 | 0.97 | [-0.67,  2.63] | 86.88% | 1.000 |  0.592

## [1] "- b_condition (Median = 6.77, 90% CI [3.84, 9.34]) has a 100.00% probability of being positive (> 0), 99.94% of being significant (> 1.05), and 62.62% of being large (> 6.29)"
## [2] "- b_hungry (Median = 4.63, 90% CI [2.77, 6.57]) has a 100.00% probability of being positive (> 0), 99.88% of being significant (> 1.05), and 8.50% of being large (> 6.29)"

## 
## ------ ------ -------------- -------
##  ICC    N id   Observations    R2   
## 
##  0.55    50        184        0.681 
## ------ ------ -------------- -------

Plot Perceived liking (Pavlovian Cue)

1. Posterior distribution by Pavlovian cue. B) Highest density interval (90% HDI) of the posterior distribution difference for the latency to respond between CS+ and CS-

Instrumental Conditioning Task

grips = number of times participant exceeded the force threshold to acquire the reward (Milkshake)

Model Comparison between linear and piecewise with spline regression
Best fit => Piecewise Regression with spline: smaller ELPD (expected log pointwise predictive density estimated via leave-one-out cross-validation) is better

## 
## ----------------------------------------------------
##    model     elpd_diff   se_diff   looic   se_looic 
## ----------- ----------- --------- ------- ----------
##  splinemod       0          0      11921     93.6   
## 
##   linmod      -1.103      3.034    11923    93.47   
## ----------------------------------------------------

## [1] "Bayesian linear mixed model (estimated using MCMC sampling with 4  chains of 500  iterations and a warmup of 100 ) to predict grips with trial, intervention, session, age, gender, BMI_V1, hungry, GLP_diff and reelin_diff (formula: grips ~ lspline(trial, 5) + intervention + session + age + gender + BMI_V1 + hungry + GLP_diff + reelin_diff + lspline(trial, 5):intervention + lspline(trial, 5):session + intervention:session + lspline(trial, 5):intervention:session). The model included session, id and trial as random effects (formula: list(~session | id, ~1 | trial)). Priors over parameters were set as normal (mean = 0.00, SD = 3.00), and student_t (location = 0.00, scale = 8.90) distributions"

## Summary of Posterior Distribution
## 
## Parameter                    | Median |  MAD |         90% CI |     pd |  Rhat |     BF
## ---------------------------------------------------------------------------------------
## trial<5                      |   0.06 | 0.09 | [-0.09,  0.23] | 74.69% | 1.001 |  0.036
## trial>5                      |  -0.12 | 0.02 | [-0.14, -0.09] |   100% | 1.000 | > 1000
## intervention                 |  -1.73 | 1.01 | [-3.45, -0.19] | 96.00% | 1.000 |   1.50
## session                      |   1.27 | 0.52 | [ 0.41,  2.10] | 99.62% | 0.998 |   4.40
## age                          |  -1.03 | 0.83 | [-2.42,  0.36] | 89.12% | 0.998 |  0.611
## gender                       |  -0.31 | 0.96 | [-1.86,  1.20] | 62.81% | 1.001 |  0.332
## BMI_V1                       |  -1.38 | 0.98 | [-2.79,  0.39] | 91.19% | 1.003 |  0.722
## hungry                       |  -0.17 | 0.68 | [-1.38,  0.79] | 59.62% | 1.002 |  0.253
## GLP_diff                     |   1.18 | 1.16 | [-0.72,  3.17] | 84.12% | 1.001 |  0.666
## reelin_diff                  |   0.24 | 1.36 | [-1.95,  2.47] | 57.69% | 1.001 |  0.477
## trial<5:intervention         |   0.09 | 0.08 | [-0.05,  0.21] | 86.88% | 0.999 |  0.050
## trial>5:intervention         |   0.02 | 0.01 | [ 0.00,  0.05] | 97.69% | 1.001 |  0.039
## trial<5:session              |  -0.19 | 0.08 | [-0.31, -0.05] | 99.38% | 0.999 |  0.461
## trial>5:session              |   0.02 | 0.01 | [ 0.00,  0.04] | 92.38% | 1.000 |  0.013
## intervention:session         |   0.24 | 0.52 | [-0.59,  1.15] | 69.12% | 0.998 |  0.184
## trial<5:intervention:session |  -0.12 | 0.07 | [-0.24,  0.02] | 93.88% | 0.999 |  0.099
## trial>5:group:session        |  -0.02 | 0.01 | [-0.04,  0.00] | 96.69% | 1.000 |  0.025

## [1] "- b_lsplinetrial51 (Median = 0.06, 90% CI [-0.09, 0.23]) has a 74.69% probability of being positive (> 0), 0.31% of being significant (> 0.37), and 0.00% of being large (> 2.22)"     
## [2] "- b_lsplinetrial52 (Median = -0.12, 90% CI [-0.14, -0.09]) has a 100.00% probability of being negative (< 0), 0.00% of being significant (< -0.37), and 0.00% of being large (< -2.22)"
## [3] "- b_intervention (Median = -1.73, 90% CI [-3.45, -0.19]) has a 96.00% probability of being negative (< 0), 91.31% of being significant (< -0.37), and 31.56% of being large (< -2.22)" 
## [4] "- b_session (Median = 1.27, 90% CI [0.41, 2.10]) has a 99.62% probability of being positive (> 0), 96.62% of being significant (> 0.37), and 3.75% of being large (> 2.22)"

## 
## ------ ------ --------- -------------- -------
##  ICC    N id   N trial   Observations    R2   
## 
##  0.79    50      24          2232       0.789 
## ------ ------ --------- -------------- -------

Plot

Number of grips over trials by session.

Pavlvovian-Instrumental Transfer (PIT) Task

Mobilized effort = Area under the curve of the force exerted exceeding the delivery threshold during Pavlovian cue presentation

## [1] "Bayesian general linear mixed model (hurdle gaussian family with a identity link) (estimated using MCMC sampling with 4  chains of 500  iterations and a warmup of 100 ) to predict Mobilized Effort (AUC) with condition, intervention, session, age, gender, BMI_V1, hungry, GLP_diff and reelin_diff (formula: AUC ~ condition * intervention * session + age + gender + BMI_V1 + hungry + GLP_diff + reelin_diff). The model included condition, session, id and trialxcondition as random effects (formula: list(~condition * session | id, ~1 | trialxcondition)). Priors over parameters were set as normal (mean = 0.00, SD = 3.00), and student_t (location = 0.00, scale = 130.20) distributions"

## Summary of Posterior Distribution
## 
## Parameter                      | Median |  MAD |        90% CI |     pd |  Rhat |    BF
## ---------------------------------------------------------------------------------------
## condition                      |   3.17 | 2.02 | [-0.54, 6.24] | 92.44% | 1.007 |  2.33
## intervention                   |   0.74 | 2.59 | [-3.40, 5.38] | 61.19% | 1.008 | 0.886
## session                        |   0.02 | 2.91 | [-4.84, 4.63] | 50.25% | 1.039 |  1.08
## age                            |   1.19 | 3.22 | [-3.93, 6.28] | 66.00% | 1.035 |  1.22
## gender                         |   0.53 | 2.85 | [-4.25, 5.46] | 56.56% | 1.006 | 0.964
## BMI_V1                         |   0.03 | 3.01 | [-4.44, 5.86] | 50.38% | 1.009 |  1.09
## hungry                         |  -0.43 | 2.91 | [-4.80, 4.52] | 56.12% | 1.012 |  1.03
## GLP_diff                       |   1.06 | 2.89 | [-4.64, 5.57] | 63.00% | 1.009 |  1.13
## reelin_diff                    |   0.53 | 3.00 | [-4.61, 5.08] | 57.31% | 1.010 | 0.990
## condition:intervention         |   0.76 | 1.95 | [-2.23, 4.59] | 64.19% | 1.007 | 0.715
## condition:session              |  -0.20 | 1.71 | [-3.04, 2.73] | 55.62% | 1.001 | 0.610
## intervention:session           |  -0.78 | 2.68 | [-5.31, 3.70] | 62.62% | 1.008 | 0.841
## condition:intervention:session |   0.70 | 1.75 | [-1.99, 3.59] | 66.12% | 1.004 | 0.579

## [1] "- b_condition (Median = 3.17, 90% CI [-0.54, 6.24]) has a 92.44% probability of being positive (> 0), 92.31% of being significant (> 0.05), and 90.56% of being large (> 0.30)"

## 
## ------ ------ ------------------- -------------- -------
##  ICC    N id   N trialxcondition   Observations    R2   
## 
##  0.70    50           15               2760       0.709 
## ------ ------ ------------------- -------------- -------

Plot

1. Posterior distribution by group. B) Highest density interval (90% HDI) for the interaction condition by session

Mobilized effort for each condition and group over trials.

Hedonic Reactivity Test

Perceived liking = how pleasant is the liquid solution rated (0-100, with repetitions) & condition = Milshake or Tasteless & intensity = difference on how intense the liquid solution were rated (mean(Milshake) - mean(Tasteless)) & familiarity = difference on how familiar the liquid solution were rated (mean(Milshake) - mean(Tasteless))

## [1] "Bayesian general linear mixed model (hurdle gaussian family with a identity link) (estimated using MCMC sampling with 4  chains of 500  iterations and a warmup of 100 ) to predict Perceived Liking with condition, intervention, session, age, gender, BMI_V1, hungry, GLP_diff and reelin_diff (formula: perceived_liking ~ condition * intervention * session + age + gender + BMI_V1 + hungry + GLP_diff + reelin_diff + int + fam). The model included condition, session, id and trialxcondition as random effects (formula: list(~condition | id, ~1 | trialxcondition)). Priors over parameters were set as normal (mean = 0.00, SD = 3.00) and student_t (location = 0.00, scale = 31.7) distributions for beta and sd respectively"

## Summary of Posterior Distribution
## 
## Parameter                      | Median |  MAD |         90% CI |     pd |  Rhat |     BF
## -----------------------------------------------------------------------------------------
## condition                      |  12.99 | 1.78 | [10.00, 15.73] |   100% | 1.006 | > 1000
## intervention                   |   1.41 | 1.64 | [-1.40,  4.07] | 79.00% | 1.006 |  0.863
## session                        |   1.29 | 1.01 | [-0.32,  2.95] | 90.00% | 1.001 |  0.850
## age                            |  -0.46 | 1.50 | [-2.91,  2.32] | 62.75% | 1.004 |  0.583
## gender                         |  -2.14 | 1.54 | [-4.66,  0.29] | 92.00% | 1.002 |   1.54
## BMI_V1                         |   2.14 | 1.61 | [-0.62,  4.78] | 90.62% | 1.002 |   1.38
## hungry                         |   1.38 | 1.30 | [-0.70,  3.41] | 84.38% | 1.007 |  0.693
## GLP_diff                       |  -0.65 | 1.96 | [-3.53,  2.74] | 63.06% | 1.000 |  0.707
## reelin_diff                    |  -2.38 | 2.03 | [-5.67,  1.07] | 87.25% | 1.009 |   1.63
## int                            |   0.68 | 2.51 | [-3.16,  4.75] | 61.19% | 1.016 |  0.880
## fam                            |   0.90 | 1.59 | [-1.70,  3.53] | 71.00% | 1.004 |  0.633
## condition:intervention         |   2.58 | 1.47 | [-0.26,  4.85] | 93.69% | 1.000 |   2.03
## condition:session              |  -0.63 | 0.87 | [-1.97,  0.97] | 75.75% | 1.004 |  0.427
## intervention:session           |   0.12 | 0.85 | [-1.24,  1.69] | 54.94% | 1.002 |  0.289
## condition:intervention:session |   0.60 | 0.82 | [-0.84,  1.95] | 76.75% | 1.000 |  0.404

## [1] "- b_condition (Median = 12.99, 90% CI [10.00, 15.73]) has a 100.00% probability of being positive (> 0), 100.00% of being significant (> 0.05), and 100.00% of being large (> 0.30)"

## 
## ------------------- -------------- ------------------------------ ---- ----
##  N trialxcondition   Observations   Marginal R2 / Conditional R2   NA   R2 
## 
##         20               3680              0.284 / 0.798           NA   NA 
## ------------------- -------------- ------------------------------ ---- ----

Plot

1. Posterior distribution by group. B) Highest density interval (90% HDI) for the interaction condition by session

Perceived liking for each condition and group over trials.

Packages

##   - repro (version 0.1.0; Aaron Peikert, Andreas Brandmaier and Caspar van Lissa, 2020)
##   - ggpubr (version 0.4.0; Alboukadel Kassambara, 2020)
##   - papaja (version 0.1.0.9997; Aust et al., 2020)
##   - tinylabels (version 0.2.1; Barth, 2021)
##   - cowplot (version 1.1.1; Claus Wilke, 2020)
##   - apaTables (version 2.0.8; David Stanley, 2021)
##   - Rcpp (version 1.0.6; Dirk Eddelbuettel and Romain Francois, 2011)
##   - Matrix (version 1.2.18; Douglas Bates and Martin Maechler, 2019)
##   - lme4 (version 1.1.27; Douglas Bates et al., 2015)
##   - XML (version 3.99.0.6; Duncan Temple Lang, 2021)
##   - intmed (version 0.1.2; Gary Chan, 2020)
##   - pander (version 0.6.3; Gergely Daróczi and Roman Tsegelskyi, 2018)
##   - ggplot2 (version 3.3.3; Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.)
##   - plyr (version 1.8.6; Hadley Wickham, 2011)
##   - stringr (version 1.4.0; Hadley Wickham, 2019)
##   - tidyr (version 1.1.3; Hadley Wickham, 2021)
##   - usethis (version 2.0.1; Hadley Wickham and Jennifer Bryan, 2021)
##   - devtools (version 2.4.2; Hadley Wickham, Jim Hester and Winston Chang, 2021)
##   - dplyr (version 1.0.6; Hadley Wickham et al., 2021)
##   - kableExtra (version 1.3.4; Hao Zhu, 2021)
##   - afex (version 0.28.1; Henrik Singmann et al., 2021)
##   - ggthemes (version 4.2.4; Jeffrey Arnold, 2021)
##   - optimx (version 2020.4.2; John Nash, Ravi Varadhan, 2011)
##   - cmdstanr (version 0.3.0.9000; Jonah Gabry and Rok Češnovar, 2020)
##   - JWileymisc (version 1.2.0; Joshua Wiley, 2020)
##   - tidybayes (version 2.3.1; Kay M, 2020)
##   - MBESS (version 4.8.0; Ken Kelley, 2020)
##   - tibble (version 3.1.2; Kirill Müller and Hadley Wickham, 2021)
##   - rlist (version 0.4.6.1; Kun Ren, 2016)
##   - sjPlot (version 2.8.8; Lüdecke D, 2021)
##   - bayestestR (version 0.10.0; Makowski et al., 2019)
##   - coda (version 0.19.4; Martyn Plummer et al., 2006)
##   - caret (version 6.0.88; Max Kuhn, 2021)
##   - lspline (version 1.0.0; Michal Bojanowski, 2017)
##   - brms (version 2.15.0; Paul-Christian Bürkner, 2017)
##   - R (version 4.0.1; R Core Team, 2020)
##   - psych (version 2.1.3; Revelle, 2020)
##   - BayesFactor (version 0.9.12.4.2; Richard Morey and Jeffrey Rouder, 2018)
##   - emmeans (version 1.6.1; Russell Lenth, 2021)
##   - Rmisc (version 1.5; Ryan Hope, 2013)
##   - janitor (version 2.1.0; Sam Firke, 2021)
##   - lattice (version 0.20.41; Sarkar, Deepayan, 2008)
##   - corrplot (version 0.89; Taiyun Wei and Viliam Simko, 2021)
##   - knitr (version 1.33; Yihui Xie, 2021)